Davis will be making her Broadway debut when she replaces Kerry Butler on July 10 as a politician's wife in the Gore Vidal play.
Stamos and the Sex and the City star will be joined by Cybill Shepherd and Tony Award winner Elizabeth Ashley.
The new additions to The Best Man ensemble coincide with the departures of Angela Lansbury, Eric McCormack and Candice Bergen.
James Earl Jone, John Larroquette and Jefferson Mays are currently in The Best Man cast and will remain until the show closes in September.
Gore Vidal's The Best Man earned two nominations at last weekend's Tony Awards, including a nod in the 'Best Revival Of A Play' category.
McCormack previously described the main antagonist of The Best Man as a cross between Mad Men's Don Draper and former Republican presidential candidate Rick Santorum.